The Matrix

This is weirdly RSA, but in a “matrix” context. To decrypt message in RSA, we need to calculate $m = c ^ d \mod p$, where $d = e ^ {-1} \mod \phi(n)$. $\phi(n)$ is the multiplicative order of the group. In this challenge, we are under some group of matrix with size 50x50, or in math notations, $GF(50, GF(2))$ and not under $\mod n$. Thus, $d = e ^ {-1} \mod |G|$, where $|G|$ is the order of the group $GF(50, GF(2))$....